Further improvement might be obtained from iteratively generated balanced winds [ Randel, 1987], but the nonlinear balance approximation was often found not to converge [ Boville, 1987; Verkhoglyadova et al., 2014].
It is concluded that the conventional harmanic-balance approximation is reliable over the stable segments of the resonance curve, but that it may not provide a satisfactory approximation to the symmetry-breaking bifurcation.
To facilitate the understanding of the nonlinear circuit effect on the behavior of the coupled harvester-structure system under sinusoidal excitation, a first-order harmonic balance approximation method is employed.
The existence of stable subharmonic motions found is confirmed by solving the differential equation of motion numerically by means of a time-difference method, with initial conditions being supplied by the harmonic balance approximation.
The sequences (cascades) of harmonic and subharmonic stationary solutions to the equation of motion are obtained by using the harmonic balance approximation adapted for arbitrary truncation numbers, powers of non-linearity, and orders of subharmonics.
In general, the concentration of specific metabolites may be high enough relatively to the fluxes they are involved in for the mass balance approximation to become clearly false.
Here, μ > 0 is a regularisation parameter which balances the approximation error and sparseness of Φ and imposes a unique solution.
For the subdivision schemes, pseudo splines provide various choices that meet different demands for balancing the approximation power, the length of the support, and the regularity of the limit functions.
From the perspective of quantitative modeling using flux balance approximations, the solvent capacity constraint forces us to consider reaction kinetics via the crowding coefficients, at least for fast growing cells.
The Singular perturbation approximation balanced truncating technique is found to give the lowest modelling errors in low frequency ranges and hence is deemed most suitable for controller design and other real-time applications.
We also propose a simple technique to construct a well-balanced approximation of the dominant hydrostatics that, if not properly discretized, may cause unacceptable vertical oscillations.
